The 23-year-old Austrian, ranked a career-high seventh, and 20-year-old German Alexander Zverev, who reached a career-best eighth on Monday, are the top-ranked men's players at the ATP and WTA Citi Open.
"We still have to win a lot of matches to deserve to be called the next big things in tennis," Thiem said Monday. "It's nice to hear that but I think it's still a pretty long ways for both of us."
World number one Andy Murray, second-ranked Rafael Nadal, number three Roger Federer and Novak Djokovic, who will miss the rest of the year with an elbow injury, remain the gold standard in their 30s that Thiem and his fellow 20-somethings are chasing in the rankings and for Grand Slam crowns.
"They are really special. It's very unusual you have four players like this in one generation," Thiem said.
"I think it's getting a little better for the other players. They are starting to take a few tournaments. In the Grand Slams you would have to beat two or three (of them) in a run. That's why other players haven't won the big titles."
Thiem defeated Djokovic in the French Open quarter-finals to reach the last four at Roland Garros for the second consecutive year.
He lost there to Rafael Nadal, as he had in the Madrid and Barcelona finals, but Thiem recognizes the value of a strong run-up to a Slam with the US Open looming in just four weeks.
"It's important to find a strong game. It's the start of a very long journey," Thiem said.
"I hope it works out well here in Washington. We have a lot of tough matches ahead. From round one basically there are only really tough matches."
This week is Thiem's biggest event as a top seed and one he expects will toughen him for upcoming US Open tune-ups at Montreal and Cincinnati.
"Of course it's nice to be top seed here but it doesn't affect anything because the guys behind me are really strong," he said.
Thiem does not marvel at how players like Federer and Nadal play top tennis deep into their 30s, having followed their fitness path.
"It's everything on how you are taking care of your body," he said. "Players have improved that a lot in recent years. It's the diet. Everyone has a physio. They get treatment after every practice.
"It's small things but if you do them every day for 15 years it has an impact."
Related slideshow: Men's Grand Slam winners (provided by photo services)
Men's Grand Slam Winners